For example, this graph shows the inequality \(x \textless -1\). This can be seen as there is a dashed line at \(x = -1\), and the region where the \(x\) coordinates are less than -1 is shaded.

A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(f(x) = x^2\) is the same as the graph of \(y = x^2\).

Examines graph theory, trees, algebraic systems, Boolean algebra, groups, monoids, automata, machines, rings and fields, applications to coding theory, logic design ...